1 lbs zucchini or summer squash
1 1/4 teaspoons salt
1 bunch basil, leaves torn
1 oz Parmesan, coarsely grated (on large holes of a box grater; 1/2 cup)
3 tablespoons extra-virgin olive oil
1/4 teaspoon black pepper
Cut zucchini crosswise into paper-thin slices with slicer or vegetable peeler.
Toss zucchini slices with 1 teaspoon salt in a large colander set over a bowl and let drain 20 minutes.
Rinse zucchini slices well, then drain, pressing gently on slices to extract any excess liquid. Pat zucchini slices dry with a kitchen towel.
Put basil leaves in a large bowl. Sprinkle with 1/4 cup Parmigiano-Reggiano and remaining 1/4 teaspoon salt. Drizzle 1 1/2 tablespoons of oil over greens and toss.
Arrange zucchini slices over arugula greens, then drizzle with remaining oil and sprinkle with remaining 1/4 cup Parmigiano-Reggiano and pepper.